Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

翻译：现实世界的时间序列数据中存在不规则的采样间隔和缺失值，这对假设恒定间隔和完整数据的传统方法构成了挑战。神经常微分方程（Neural ODEs）提供了一种替代方法，通过使用神经网络结合ODE求解器，学习由参数化向量场驱动的连续潜在表示。神经随机微分方程（Neural SDEs）通过引入扩散项扩展了Neural ODEs，然而这一扩展并非易事，尤其是在处理不规则间隔和缺失值时。因此，谨慎设计漂移函数和扩散函数对于保持稳定性和提升性能至关重要，而不当的选择可能导致不良性质，例如缺乏强解、随机失稳或不稳定的欧拉离散化，从而显著影响Neural SDEs的性能。在本研究中，我们提出了三类稳定的Neural SDEs：朗之万型SDE、线性噪声SDE和几何SDE。随后，我们严格证明了它们在分布偏移下保持优异性能的鲁棒性，同时有效防止过拟合。为评估所提方法的有效性，我们在四个基准数据集上进行了插值、预测和分类任务的大量实验，并在30个公共数据集上分析了不同缺失率下方法的鲁棒性。结果表明，所提方法在处理现实世界的不规则时间序列数据方面具有显著效能。